Method for seismic exploration

ABSTRACT

Sweeps of seismic signals consisting of pulse trains having a predetermined number of pulses in which the periods or durations of the pulses are randomized and in which the wave shape and relative time displacements of the pulses in different trains provides substantially constant spectral level over a frequency range containing several octaves.

BACKGROUND OF THE INVENTION

The present invention relates to methods and apparatus for thetransmission of signals useful in seismic exploration both on land andin water covered areas, and also to methods and apparatus for derivinginformation from the cross correlation of the transmitted signals whichare received after reflection from geological interfaces with replicasof the transmitted signals so as to delineate reflecting surfaces atdifferent penetrations into the formation with high resolution.

In the search for high resolution seismograms, various types of signalshave been designed for transmission into the ground in the form ofacoustic energy. Classically these signals have been sinusoids whichsweep in frequency linearly and monotonically with time (see, D. L.Goupillaud, Signal Design in the "Vibroseis" Technique, Geophysics, Vol.41, No. 6, 1291-1304, December 1976. D. E. Nelson (U.S. Pat. No.4,204,278, issued May 20, 1980), has described a signal design which canbe generated and transmitted for geophysical exploration into the groundutilizing quasi-periodic pulse trains which are swept in repetitionfrequency over an octave monotonically and combined with thetransmission through the medium (viz, after reflection from thegeological reflecting surfaces) from which high resolution and accurateseismograms can be generated.

It has been found in accordance with this invention that a signal, withthe energy content of Nelson's signal, and containing exactly the samepulses may be randomized (or pseudo randomized) such that itsconstituent parts (the individual durations or periods which vary intheir time length, each constituting a signal making up the sweep ortransmission) occur in differently scrambled order in each sweep and insuccessive sweeps so that no two sweeps in a set of sweeps aresubstantially correlated thereby to preclude false target indicationsand information that might erroneously locate or obscure geologicalreflecting surfaces. A signal provided in accordance with this inventionwhen transmitted into the ground and received by receptors (for examplein an array of geophones or hydrophones) possesses important advantagesarising out of a lack of correlation between successive lengths (thepluralities of signals) which make up the sweeps or successive sweeps.These advantages include: (a) The ability to derive information from thereceived signals in which the shot point spacing and common depth point(CDP) multiplicity may be selected as desired after the survey isperformed and may vary for different parts of the section; (b) Theability to sum the auto correlation functions (the cross correlationoutput of each sweep after transmission through the medium with itsreplica) and provide side lobes adjacent to the main lobe which are ofthe same order of amplitude as obtained with a monotonic sweep or less;and (c) The generation of side lobes in the correlation functions whichare uncorrelated from sweep to sweep in successive seismograms, whichwith monotonic sweeps would be correlated, thereby further reducingside-lobe amplitude in gummed or stacked traces.

While various pseudo random sequences of sinusoidal waves or pulses havebeen proposed, neither the randomization of the signals in thetransmission to preclude cross correlation both internally in a sweepand between successive sweeps nor the randomization of the signals in atransmission, as defined by Nelson, has even been suggested as beingpossible or practicable (see the article by P. L. Goupillaud referencedabove and Crook et al, U.S. Pat. No. 3,264,606, issued Aug. 2, 1966;Forrester, U.S. Pat. No. 326,320 issued June 20, 1967; Barbier et al,U.S. Pat. No. 3,811,111 issued May 14, 1974; Barbier, U.S. Pat. No.3,956,730, issued May 11, 1976; and Barbier, U.S. Pat. No. 4,011,924issued Mar. 15, 1977).

In the randomization proposed by Goupillaud, because the successivepulses after randomization do not join smoothly at pulse boundaries,spurious frequencies are generated and the frequency range of the sweepdiffers from that of the monotonic sweeps. Thus the amplitude spectrumof two "randomized" sweeps intended to have the same range, will in factbe different. The orthogonality of randomized sweeps as suggested byGoupillaud is governed by pure chance and may in any given instance notbe valid.

Accordingly, it is the principal object of the present invention toprovide improved methods and apparatus for the transmission of signalssuitable for seismic exploration and geophysical prospecting both onland and in water covered areas.

It is another object of the present invention to provide improvedmethods and apparatus for seismic prospecting in which the seismicsignals are transmitted and processed so as to obtain seismograms havingselected shot point spacing, sweep duration, and CDP multiplicity fromthe same transmission and without having to repeat the transmission.

It is a further object of the present invention to provide improvedmethods and apparatus for the transmission of seismic signals whichenables the sweep duration to be selected either upon transmission orduring processing after the survey is performed so as to obtaininformation in which the necessary compromise between the resolution,penetration and signal to noise ratio yields optimum results.

It is a still further object of this invention to provide a method ofgenerating and applying a set of distinctly different, mutuallyorthogonal, seismic signals all having the same amplitude spectra.

SUMMARY OF THE INVENTION

Briefly described, the invention may for example be used in methods andapparatus for transmitting seismic signals which change in duration by afactor not exceeding two to one (a frequency change not exceeding anoctave) during a sweep. The invention improves such signals bygenerating a predetermined number of them of different duration duringthe sweep and randomizing the occurrence of these signals of differentduration such that none of these signals repeats or are missing duringthe sweep. The cross correlation of any successive pluralities of thesignals within the sweep or in successive sweeps which may betransmitted such that signals from successive sweeps may be received ata receiving location during the same period of time, do not providesignificant cross correlation outputs (they are essentially orthoganal).Further, in accordance with the invention, the cross correlation of thesignals that are received after transmission through the medium may becarried out with less than all of the signals in the sweep. This enableseffectively varying the shot point spacing of the sweeps and, of course,the CDP multiplicity so as to obtain the needed resolution, penetrationand signal-to-noise ratio for any section of the seismogram.

The randomized sequences of signals also include sequences which may bedeemed pseudo-random in that the order of pulses in each sweep isscrambled in accordance with a predesigned system to improveorthogonality among the sweeps.

By applying the randomization process to pulses such as those disclosedby Nelson, the joints between successive pulses are smooth and do notcontribute spurious frequencies to the amplitude spectrum of theresulting sweep signal.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, features and advantages of theinvention as well as the preferred embodiment of the invention and thebest mode presently known for carrying out the invention will becomemore apparent from a reading of the following description in connectionwith the accompanying drawings in which:

FIG. 1 is a block diagram schematically illustrating apparatus embodyingthe invention and by means of which the invention may be practiced; and

FIG. 2 shows auto correlation functions of signals which may begenerated and transmitted in accordance with the invention.

DETAILED DESCRIPTION

Referring more particularly to FIG. 1, there is shown a store 10 of thesuccessive numbers 1 to n in a succession of randomized orders. Asuitable store may be read-only memory generally known as a ROM or aPROM. One randomized set of signals corresponding to numbers from 1 to nis known as a sweep. A typical sweep may be ten seconds in time lengthand have 196 signals. These signals are formed from a plurality of pulsetrains S1, S2, S3, S4, S6, and S6. A seismic source or preferably aplurality of seismic sources 12 are driven by these signals, S1 throughS6, to provide the transmission of the signals in the form of acousticsignals corresponding thereto. The sources 12 which are used depend onwhether the signals are to be transmitted directly into the earthformation on land or into the earth formation via water, as in watercovered areas. The nature of the sources 12 and the nature of thesignals in each duration or period which constitute unique ones of the196 signals in this example are described in the above referenced NelsonU.S. Pat. No. 4,204,278. Each signal has a duration which is referred toas a fundamental period in the Nelson patent. The time length of thesignals (their periods) vary monotonically in the Nelson patent with theratio of the duration from the longest to the shortest signal notexceeding a factor of two to one. The repetition frequency of thesignals in a sweep, thus does not exceed an octave in frequency range.The same octave frequency range is covered by the signals produced andtransmitted with the apparatus shown in FIG. 1. However, differentsignals (signals which are of different duration and are different onesof the 196 signals) are scrambled or randomized and transmitted in therandom order. This randomizing of the signals results in the advantagesobtained by the invention.

The numbers stored in store 10 consist of a preselected small number ofpremutations of the number n of signals of different length selected fora sweep. If the number of different permutations selected is only two, aconvenient selection may be made by using any order whatsoever, even amonotonic increasing sequence, and the same order reversed. For exampleif n=4 the first order may be 1342 and the second 2431. It is readilyapparent that no two numbers in the first set are in the same order asthose in the second set hence the sweeps generated from the two setswill be uncorrelated at all but a maximum of one signal for all relativedisplacements of the two sweeps, hence the cross correlation of the twosweeps will be a minimum. Otherwise stated, the two sweeps areorthogonal.

This concept will be better understood by reference to the followingschematic table for the above example in which n=4 (for simplicitycorrelations have not been divided by a normalizing factor).

    ______________________________________                                        S.sub.3 S.sub.3 S.sub.4 S.sub.2                                                                  Correlation value: .sub.2 S.sub.1 S.sub.2 + .sub.2                            S.sub.3 S.sub.4                                            S.sub.2 S.sub.4 S.sub.3 S.sub.1                                               S.sub.1 S.sub.3 S.sub.4 S.sub.2                                                                  Correlation value: .sub.2 S.sub.2 S.sub.3                                     + S.sub.4.sup.2                                            S.sub.2 S.sub.4 S.sub.3 S.sub.1                                               S.sub.1 S.sub.3 S.sub.4 S.sub.2                                                                  Correlation value: .sub.2 S.sub.2 S.sub.4                  S.sub.2 S.sub.4 S.sub.3 S.sub.1                                               S.sub.1 S.sub.3 S.sub.4 S.sub.2                                                                  Correlation value: S.sub.2.sup.2                           S.sub.2 S.sub.4 S.sub.3 S.sub.1                                               ______________________________________                                    

It will be noted that none of the correlations contains more than onesquared value. That condition is referred to herein as orthogonalitybetween the two sweeps.

To generate a set of orthogonal sweeps for any n, the following methodmay be used.

First, write the numbers from 1 to n in increasing monotonic order. Forexample if n=10: 1,2,3,4,5,6,7,8,9,10.

Second, write a new set beginning with 2 and successively add 2 to eachpreceding number. If a number exceeds n, subtract (n+1) from it. In theexample: 2,4,6,8,10,1,3,5,7,9. Third, write a new set beginning with 3and successively add 3 to each preceding number. Again if a numberexceeds n, subtract (n+1) from it. In the example: 3,6,9,1,4,7,10,2,5,8.Continue in this fashion until n is the beginning number in thesequence.

If n+1 is a prime number, all of the n generated sequences will beorthogonal to each other. If n+1 is not a prime number the rule must bemodified by requiring the addition of 1 when a zero or a previouslyobtained number is generated. Only some of the sequences generated forn+1 not a prime will form an orthogonal set. Which ones are to berejected from the set can be determined by examination. For most cases,n-1 sequences will be found to form an orthogonal set.

It will be noted that exemplary number n=196 is such that n+1=197, aprime number. Since in practice the number n can be chosen withinsubstantial limits, either by slightly modifying the desired frequencyrange or the sweep duration, it is usually convenient to select n suchthat n+1 is prime, thereby eliminating a somewhat tedious examination ofthe generated sequences. If a digital computer is available, theexamination of the generated set of sweeps becomes a trivial exerciseand n may be conveniently selected without regard to the primality ofn+1.

All or a selected smaller number of the generated sequences are storedin store 10 to be fed to reciprocal generator 18 as will be describedbelow. It will generally be useful to reject the first and lastsequences generated by the above described process since those aremonotonic. The side lobes occurring in the autocorrelations of thesecond and the penultimate sequences will be lower than those in the twomonotonic sequences. If n is quite large, say substantially more thanabout 10, the third and the antepenultimate sequences will have evenlower autocorrelation side lobes. If a computer is available, anexhaustive search may be used to further optimize the selected set ofsequences to reduce to a minimum the cross correlations of the selectedsequences with each other.

To those skilled in those branches of mathematics that deal with sets,it will be apparent that a considerable variety of different sets oforthogonal sequences may be generated from the sets generated asdescribed hereinabove by different one-to-one mappings of the set ofintegers from one to n onto itself.

The output of the store for any sweep j is a sequence of numbers n shownas T_(j), T_(j+1) . . . T_(j+n). These numbers are digital numbers whichmay be eight bits in length where n is 196. The numbers are appliedsuccessively to a reciprocal generator 18 which generates a reciprocalof these numbers 1/T_(j), 1/T_(j+1) . . . 1/T_(j+n). A digital to anlogconvertor (DAC) 20 converts the value represented by each of thesenumbers into a control voltage which is applied to a voltage controlledoscillator (VCO) 22. The VCO 22 outputs a pulse train which at itslowest repetition frequency is the repetition frequency of the low endof the sweep multiplied by a factor depending upon how many periods ofthe pulse train from the VCO 22 are needed to generate the signals S1 toS6 in the 1/3 period generators, dividers and delay circuits 24. In thisexample, this factor is twelve. The repetition frequency of the pulsetrain produced by the VCO 22 at the highest repetition frequency of thesweep is also multiplied by the same factor. The repetition frequencyvaries over an octave frequency range, for example, from five to tenHertz or from ten to twenty Hertz in a typical application of theillustrated apparatus. Each time twelve pulse periods are generated, adivider 26 outputs a command to advance the store 10 to produce the nextsignal period.

The VCO 22 operates in a manner similar to the VCO 101 in the circuitdescribed in connection with FIG. 5 of the Nelson U.S. Pat. No.4,204,278. The generators 10 and 16, the number ordering logic 14, thereciprocal generator 18, the DAC 20 and the divider 26 serve a functionin the nature of the function provided by the ramp generator 102 inNelson FIG. 5; however, instead of a monotonic sweep the signals in thesweep have different durations and are randomized. The 1/3 periodgenerators, dividers and delay circuits may suitably be those describedin connection with FIG. 5 of the referenced Nelson patent. Therefore,the signals S1 to S4 which have been divided down in the dividers of thecircuits 24 are each the longest duration and define the fundamentalperiod which is the duration of each of the signals of the 176 signalswhich make up a sweep. The periods of these pulses in each duration arethe same and are indicated as P. The signal S5 is half the duration ofthe signals S1, S2, S3 or S4 or P/2. The signal S6 is half the durationof the signal S5 or P/4. All of the signals are relatively delayed withrespect to each other as indicated by the terms Δt₁ through Δt₅. Inother words the signals S1 to S4 are at the fundamental repetitionfrequency while the signals S5 and S6 are twice and four times thefundamental repetition frequency, respectively. The one third periodgenerators produce these signals with a wave form with two levels whichdivide the period into proportions of one to two. For example, therelatively positive level has a duration in proportion to the relativelynegative level in a ratio of one to two. The relatively positive levelis of a duration in proportion to the total period of the signal in aratio of one to three. Accordingly, the term one third generator aptlydescribes the generation of the signals. For the signal of fundamentalS1, there are shown in FIG. 1 two wave forms in which signalscorresponding for example to numbers 1, 2, 3 and 4 are displayed in amonotonic sweep. These signals occur successively and the periods of thesignals decrease (their repetition frequency increases) as the sweepprocedes. In the randomized sweep provided in accordance with theexample the numbers corresponding to the signals and the signals as canbe seen by their fundamental periods appear in random order as the sweepproceeds. Further information as to the design of the one third periodgenerators, dividers and delay circuits 24 may be obtained by referenceto the Nelson U.S. Pat. No. 4,204,278.

The replica of the transmitted signal is obtained by means of a summingnetwork 28. The replica, the advance signal which indicates theoccurrence of the signals in each sweep and outputs from the receptors31 (the hydrophones and geophones in this spread or streamer) are allrecorded in separate channels on a multi-channel recorder 30. Each ofthese signals from each of the receptors 31 is correlated with thereplica in correlators 32. The correlations may be carried out over aset of consecutive sweeps or over individual sweeps.

If, for example, it is required to map relatively shallow geologicstrata in fine detail, the individual sweeps may be of short durationand correlation is performed with individual sweeps. If, on the otherhand, enhancement of weak reflections from great depths is required fromthe same survey, correlation may be performed with groups of successiveshort sweeps in the same manner as if each group constituted a singlelong sweep. The groups of sweeps may be disjunct or may be overlapped,for example, by using four successive sweeps as the correlation templatebut stepping ahead only two sweeps each time a correlation is performed.

By way of illustration, if the sequence of successive sweeps isdesignated A B C D E F G H I J K--correlation may be performed using thesuccesive sequences: ABCD, EFGH, etc. or alternatively ABCD, CDEF, EFGH,etc. Such correlation options will be valid particularly because thesweeps are mutually orthogonal. Random, but not necessarily orthogonal,sweeps may also be used but correlation side lobes will, in general, besomewhat higher.

In the art of geophysical exploration by the seismic reflection methodit is customary to combine or "stack" may output traces, such as theoutputs of correlators, 32 in such a way as to enhance reflectionsignals and suppress background noise. Correlation side lobes are asignificant source of such undesired noise.

FIG. 2(a) shows the autocorrelogram of a monotonic sweep as disclosed inthe Nelson patent. It is apparent that the early side lobes in thiscorrelogram are substantially stronger than are the later ones. In thecase of the autocorrelogram of the randomized sweep in (b), it is seenthat the level of both early and late side lobes is the same but thatlevel is larger than the level of the later side lobes in (a).

When, however, several autocorrelograms are stacked as shown in (c),both early and late side lobes are reduced to the level of the late sidelobes in the autocorrelogram of the monotonic sweep. Stacking ofmonotonic sweep autocorrelograms will not similarly reduce side lobesbecause, in the monotonic case, the side lobes from successive sweepsare the same and do not average out as is the case with randomizedsweeps.

The benefit of stacking in current geophysical practice will besubstantially greater than indicated by the example because aconsiderably greater number of traces are stacked.

The steps of carrying out the necessary correlations and stacking arewell known in the geophysical art and will not be described in detail.Those steps are usually carried out in well known devices such ascontroller 34, correlators 32 and geophysical data procesor 44. Thefinal output after full geophysical processing is put into graphicalform by a plotter 46.

Sound sources employing randomized orthogonal sweeps are particularlyuseful in marine surveys under each of a variety of conditions in whichimpulsive sound sources and sources employing monotonic sweeps areprecluded from operating or are severely handicapped.

There are in various parts of the world offshore areas in which a numberof seismic exploration vessels are operating at the same time. In someof these areas interference with a vessel's reception of seismic signalsfrom signals generated from other vessels can become sufficiently greatso as to require a shutdown of operations. Alternatively, vesseloperators must consult together and allocate times and areas ofoperation, a procedure that can be exceedingly costly. The problem isparticularly acute in the case of impulsive sources of high power.Interference will be reduced for swept sources but will still exist ifthe sweeps employed by those sources are monotonic. Randomized sweeps inaccordance with the present invention reduce such interference to anegligible level because all sweeps employed are orthogonal to eachother as described hereinabove. Orthogonality assures that the result ofcorrelating one sweep signal replica with another received sweep signalis very small indeed.

In the conduct of three dimensional (3/D) seismic surveys, it isnecessary to obtain data along a plurality of closely spaced parallellines. The present state-of-the-art utilizes data obtained by a singleship emitting repeated signals and towing a single hydrophone cable totraverse the desired survey lines one after another. This procedure isboth costly and time consuming. If, on the other hand, ships areequipped to emit orthogonal randomized pulse sweeps, two ships may beused simultaneously to follow parallel tracks while maintaining the samespeed and direction so that the two ships are travelling abreast. Eachship operates a sound source in accordance with its own uniquerandomized sequence which is different from or otherwise maintainedorthogonal to the sweeps employed by the other ship. As is well known inseismic surveying, two ships operating thus in parallel will cover threelines of survey, namely the line under the path of each ship and theline midway between the two ships. As a matter of fact, the two shipswill be covering the mid line between them redundantly, namely by meansof the signal emitted by the first ship and received by the second andthe signals emitted by the second ship and received by the first. Byusing orthogonal sweeps throughout, all data obtained may be sorted bymeans well known in the geophysical exploration art. After the data arerecorded and brought to a computer center the result will be to obtainthree survey lines with the two ships, thus saving both time and money.The time savings will be such that the survey can be completed inapproximately 1/3 the time required for a single ship operation, at acost of 2/3 that of a single ship operation.

Additional benefits will be obtained through the use of orthogonalrandomized sweeps relative to conventional impulsive sources byeffective immunity to external coherent noise sources from a variety oforigins. For example, own ship's noise will tend to be emitted in acombination of single frequencies and will appear in seismic records asnoise. The correlation process when swept signals are used will reducesuch interference to a relatively insignificant level. The orthogonalrandomized sweep is best suited for this purpose because sections of thesweep will not replicate segments of sinusoids as may monotonic sweeps.One common source of extraneous noise of a steady frequency is adrilling oilwell that emits a frequency dependent on the rotation rateof the drill bit. Machinery on a drilling platform will also, ingeneral, emit fixed frequency signals at a variety of frequencies, manyof which fall within or alias into the seismic band. In all such cases,the randomized orthogonal sweep will produce the optimum noisecancellation and thereby produce the best seismic results.

While this invention has been described in terms of the pulses taught inthe Nelson patent, it will be apparent to those skilled in the art thatthe principles of this invention may be applied by randomizing anyordered sequence of pulses.

From the foregoing description it will be apparent that there has beenprovided improved methods and apparatus for the generation of theseismic signals and the processing thereof which produces new andadvantageous results in providing information from which seismograms maybe constructed. Variations and modifications in the herein describedmethods and apparatus, within the scope of the invention, willundoubtedly suggest themselves to those skilled in the art. Accordingly,the foregoing description should be taken as illustrative and not in alimiting sense.

We claim:
 1. The method of forming a plurality of sweeps of signalsbased upon a predetermined set of n distinct signals, n+1 being a primenumber, so that cross correlation of any two sweeps from said pluralityis minimized, comprising the steps of:(a) forming a first sweep byordering the set of n signals in a selected first order; (b) designatingthe position of occurrence of each of said signals in said first sweepsuccessively by the successive integers from one to n forming a firstset of integers; (c) generating a second set of n integers beginningwith the number two and followed by integers successively formed byadding the number two to each preceding integer; (d) modifying saidsecond set of integers by subtracting n+1 from any such integer whichexceeds n; and (e) forming a second sweep by ordering the occurrence ofthe set of n signals in a second order in accordance with the modifiedsecond set of integers.
 2. The method of claim 1 including theadditional steps of:(f) generating additional sets of integers eachbeginning with a different number greater than two and followed byintegers successively formed by adding such different number to eachpreceding integer; (g) modifying said additional sets of integers bysubtracting n+1 from any integer in such additional sets which exceedsn; and (h) forming additional sweeps by ordering the occurrence of theset of n signals for each additional sweep in accordance within saidmodified additional sets of integers.
 3. The method of randomizing theorder of a predetermined set of n distinct pulses, n+1 being a primenumber, in each of a plurality of pulse trains so that the crosscorrelation of any two such pulse trains from said plurality isminimized, comprising the steps of:ordering the set of n pulses in aselected first order and designating each of said pulses successively bythe successive integers from one to n, generating a second set of nnumbers by beginning with a number m greater than 1 and less than n+1and successively adding the same number m to each preceding number,subtracting n+1 from any so generated number that exceeds n, and usingthe second set of numbers to determine the order of occurrence of thepredetermined set of pulses in a second order.
 4. The method of claim 3wherein the step of generating a second set of n numbers is repeated fora plurality of values of m.
 5. The method of claim 3 or 4 wherein n+1 isnot prime including the steps of:adding one when a zero or previouslygenerated number is generated in the second set of n numbers, andselecting a mutually orthogonal group of sets of n pulses from among theso generated group of sets of n pulses.